And yet advertising raises demand, which in intern causes people to offer to meet that demand which means competition, which lowers prices.
Lots of examples of this cycle you can search for.
Higher demand causes higher prices, not lower. Competition is irrelevant because startup competitors have to advertise a lot more, making their prices even higher.
That only works for smaller and unestablished brands. There are diminishing returns to the economy of scale.
Coca-cola, for example, isn't going to lower their prices in response to increased demand from their $4 billion marketing budget.